If you have one cup of coffee and one cup of creamer and you put one tablespoon of coffee into the creamer and mix it thoroughly and take a tablespoon of that mixture and put it back into the pure coffee and mix that completely, is there more coffee in the creamer or more creamer in the coffee? (Please provide explanation or proof)
2006-09-15 11:01:29 · 10 answers · asked by ice_purple969 4 in Science & Mathematics ➔ Mathematics
I am not quite sure how people are going from a denomenator of 16 in the begining and ending up with a denominator of 17 in the end. The volume does not change, just the ratios
2006-09-15 11:56:33 · update #1
The amount of coffee in the creamer is the same as the amount of creamer in the coffee. And here's why:
Say cup1 contains coffee and cup2 contains creamer.
Assume that the volume of coffee in cup1 is V and the volume of creamer in cup2 is W. Also, let v be the volume of liquid held by a tablespoon.
When you put one tablespoon of coffee into the creamer, you get the following:
Cup 1contains V - v of coffee.
Cup2 contains W of creamer + v of coffee.
Now when you take a tablespoon of that mixture and put it back into the pure coffee, you have the following:
Cup1 has V - v of coffee + v of coffee and creamer.
Cup2 has W of creamer + v of coffee - v of coffee and creamer.
Assume that the amount of coffee in v is A and the amount of creamer in v is B.
So v = A + B
So, cup1 contains:
V - v of coffee + A of coffee + B of creamer.
= (V- v+ A) of coffee + B of creamer
Cup2, on the other hand contains:
W of creamer + v of coffee - A of coffee - B of creamer
= (W - B) of creamer + (v - A) of coffee.
= (W - B) of creamer + B of coffee (because v = A + B)
As you can clearly see,
Amount of coffee creamer = Amount of creamer in coffee
= v - A or B
2006-09-15 12:46:12 · answer #1 · answered by Anonymous · 0⤊ 1⤋
There is exactly as much creamer in the coffee as there is coffee in the creamer. The easiest way to see this is to note that the volumes of creamer and coffee after the transfers are still both one cup. So whatever coffee went into the creamer has to be replaced by the same amount of creamer going into the coffee.
2006-09-15 21:05:03 · answer #2 · answered by mathematician 7 · 1⤊ 0⤋
There are 16 tablespoons in a cup. So you take one tablespoon of coffee and add it to the creamer.
You now have 17/17ths (or seventeen tablespoons) of mixture and 15/15ths (1 cup - 1 tablespoon = 15Tbsp) coffee.
Then you take 1/17th or 1 tablespoon of the mixture, which contains 1/286th (or 1/17th of 1/17th) a tablespoon of coffee, and dump that into the Coffee. So you just added 1Tbsp - 1/286th Tbsp of creamer into the coffee.
There is 1/286 more coffee in the creamer then creamer in the coffee.
2006-09-15 18:14:11 · answer #3 · answered by boter_99 3 · 0⤊ 0⤋
1 cup = 16 T (tablespoons)
16T creamer + 1 T coffee = 17T mix
1T mix = 16/17 creamer + 1/17 creamer
16T creamer + 1T coffee - 1T mix =
(16 - 16/17)T creamer + (1-1/17)T coffee
(15 1/17) T creamer + (16/17)T coffee
16 T coffee - 1T coffee + 1 T mix
15T coffee + 1/17 coffee +16/17 creamer
(15+1/17) T coffee + 16/17 creamer
(15 1/17) T coffee + (16/17) T creamer
They are both equally contaminated
2006-09-15 18:12:20 · answer #4 · answered by Jenelle 3 · 1⤊ 1⤋
Initial
Cup 1: 16 TBS of coffee
Cup 2: 16 TBS of Creamer
First mix:
Cup 1: 15 TBS of Coffee
Cup 2: 16 TBS of Creamer, 1 TBS of Coffee
Put back in the Coffee:
Cup1 : 15 TBS of Coffee + 1/17 TB Coffee + 16/17 Creamer
15 1/17 TBS Coffee, 16/17 TBS Creamer
Cup2: 16/17 TBS Coffee
15 1/17 TBS Creamer.
There is equal amounts of creamer in the coffee and coffee in the creamer.
2006-09-15 18:09:18 · answer #5 · answered by John H 3 · 1⤊ 1⤋
There is more coffee in the creamer than creamer in the coffee because you are adding pure coffee to the creamer but a mixture to the creamer
2006-09-15 18:36:17 · answer #6 · answered by MollyMAM 6 · 0⤊ 1⤋
1 cup is 16 tablespoons. So the first operation makes it so the cream has 17 tablespoons of liquid in it, and is 1/17 coffee. The coffee has 15 tablespoons of pure coffee in it. Taking a tablespoon of material out of the cream leaves it with 16 tablespoons of liquid, 1/17 coffee and 16/17 cream. You then put that tablespoon you took out into the coffee, making it back up to 16 tablespoons. That tablespoon contained 16/17 cream, so the amount of cream in the coffee cup is 16/(17*16), which is equal to 1/17.
In other words, the contaminations are both equal.
2006-09-15 18:03:07 · answer #7 · answered by Anonymous · 1⤊ 3⤋
I agree with the second answerer but in the time I spent thinking about this, now I feel like having a cup of coffee! I think ill go get one!
If the first guys to be believed I guess I was wrong but Im still having that coffee!
2006-09-15 18:08:34 · answer #8 · answered by Silva 6 · 0⤊ 1⤋
coffee in the creamer...since you put pure coffee in the creamer while you placed a mixture of both coffee and creamer in the cup of coffee...
2006-09-15 18:04:18 · answer #9 · answered by Pikachu 4 · 3⤊ 3⤋
I have no idea i would think they have an equal amount but that's probably not the answer email me the answer please.
2006-09-15 18:12:10 · answer #10 · answered by Trish H 3 · 0⤊ 2⤋